The economic value of a formation containing hydrocarbons depends on the amount of oil or gas contained in a unit volume of a subsurface reservoir, which, among other things, is a function of its porosity and its hydrocarbon saturation. Total porosity .phi..sub.t of a formation is the fraction of the formation per unit volume occupied by pore spaces. Hydrocarbon saturation S.sub.h is a fraction of the pore volume filled with hydrocarbons. In addition to porosity .phi..sub.t and hydrocarbon saturation S.sub.h, permeability k of a formation indicates the ease with which a fluid (e.g., hydrocarbons) flows through, and can be removed from, the formation. Although a large porosity usually corresponds to a large permeability, pore size, shape, and continuity also influence permeability.
There are many well-known models that allow the calculation of saturation from well logs. In shaly formations, the preferred models are the Waxman-Smits model (See, e.g., M. H. Waxman and L. J. M. Smits, "Electrical Conductivities in Oil-Bearing Shaly Sands," Society of Petroleum Engineers 42nd Annual Fall Meeting, (Oct. 1-4, 1967), and the Dual Water model (See e.g., C. Clavier, G. Coates, and J. Dumanoir, "The Theoretical and Experimental Bases for the `Dual Water` Model for the Interpretation of Shaly Sands," Society of Petroleum Engineers Transactions 6859 (1977) (hereinafter, "Clavier et al."). Both models rely on the cation exchange capacity per unit volume Q.sub.v and the formation factor F, which are not often measured downhole nor inferred directly from logging measurements.
NMR is based on the fact that the nuclei of many elements have angular momentum (hereinafter, "spin") and a magnetic moment. Nuclear spins align themselves along an externally applied static magnetic field and obtain an equilibrium condition. This equilibrium can be disturbed by a pulse of an oscillating magnetic field, which tips the spins away from the static field direction. The degree to which the spins are tipped is under the control of the experimenter as explained below.
After tipping, two things occur simultaneously. First, the spins precess around the static field at the Larmor frequency (.omega..sub.o =.gamma.B.sub.0), where B.sub.0 is the strength of the static field and .gamma. is the gyromagnetic ratio, a nuclear constant. Second, the spins return to the equilibrium condition according to a decay time known as the "spin-lattice relaxation time" or T.sub.1. T.sub.1 is controlled by the molecular environment and is typically ten to one thousand milliseconds for water in rocks.
Also associated with the spin of molecular nuclei is a second relaxation time known as "spin-spin relaxation time" or T.sub.2. At the end of a ninety degree tipping pulse, all the spins point in a common direction perpendicular to the static field, and they precess at the Larmor frequency. However, small inhomogeneities in the static field due to imperfect instrumentation or microscopic material heterogeneities cause each of the nuclear spins to precess at a slightly different rate. Therefore, after some time, the spins will not precess in unison, that is they will dephase. When dephasing is due to static field inhomogeneity of the apparatus, the dephasing time is called T.sub.2 *. When the dephasing is due to properties of the material, the dephasing time is called T.sub.2.
T.sub.2 can be several seconds in an unconfined low viscosity liquid such as water, and as short as ten microseconds in a solid. Liquids confined in the pores of rocks present an intermediate case where T.sub.2 is in the range of tens to hundreds of milliseconds, depending on various factors, such as pore size and fluid viscosity.
A known method for measuring T.sub.2 is called the Carr-Purcell-Meiboom-Gill ("CPMG") sequencing method. In solids, where T.sub.2 is very short, T.sub.2 can be determined from the decay of a detected signal after a ninety degree pulse. However, for liquids where T.sub.2 *&lt;&lt;T.sub.2, the free induction decay becomes a measurement of the apparatus-induced inhomogeneities. To measure the true T.sub.2 in such liquids, it is necessary to cancel the effect of the apparatus-induced inhomogeneities.
This cancellation is achieved by applying a sequence of pulses. The first pulse is a ninety degree pulse that causes the spins to start precessing. After the spins have begun precessing, a one hundred eighty degree pulse is applied to keep the spins in the measurement plane, but to cause the spins which are dispersing in the transverse plane to precess in the reverse direction, thereby refocusing the spins. By repeatedly reversing and refocusing the spins by one hundred eighty degree pulses, a series of "spin echoes" occur. This succession of one hundred eighty degree pulses, after the initial ninety degree pulse, is the Carr-Purcell sequence which measures the irreversible dephasing (i.e., T.sub.2) due to material properties. Meiboom and Gill devised a modification to the Carr-Purcell pulse sequence such that, after the spins are tipped by ninety degrees and start to dephase, the carrier of the one hundred eighty degree pulses relative to the carrier of the ninety degree pulse. As a result, any error that occurs during an even pulse of the CPMG sequence is canceled out by an opposing error in the odd pulse. A detailed explanation of NMR principles and pulse sequences is described in Freedman U.S. Pat. No. 5,291,137.
Unfortunately, the presence of gas in rock pores adversely effects the derivation of total formation porosity .phi..sub.t. See, e.g., Robert Freedman, Austin Boyd, Greg Gubelin, Donald McKeon, and Chris Morriss, "Measurement of Total NMR Porosity Adds New Value to NMR Logging," Paper O, Transactions of the Society of Professional Well Log Analysts 38.sup.th Annual Logging Symposium (1997).
For example, NMR-derived total porosities .phi..sub.nmr are generally underestimated when gas is present in the zone being measured. At least two effects may be responsible for the underestimation of .phi..sub.t. The first effect is related to an abnormally low hydrogen index of gas. The low index effect is familiar to log analysts because it also causes neutron tool porosities to be reduced in gas zones. The second effect is related to insufficient polarization of the gas. The insufficient polarization effect occurs because reservoir gas has longitudinal relaxation times T.sub.1 that are in the range from between 3 and 6 seconds at normal reservoir conditions. Because T.sub.1 is so long, the time required to fully polarize reservoir gas is on the order of ten seconds using conventional pulse sequences, such as the Carr-Purcell-Meiboom-Gill ("CPMG") sequences. Unfortunately, a ten second wait time is generally impractical for routine logging operations because it results in very slow logging speeds.
Many previously published methods for using NMR data to detect and quantify hydrocarbons in formations are "NMR-only" methods. That is, these methods use NMR data alone to derive hydrocarbon-related and porosity-related parameters. Most of these methods are based on concepts introduced by Akkurt et al., who recognized that the differences between the NMR properties of water and non-wetting hydrocarbons in porous rocks provides a means for distinguishing formation fluids into gas, oil, and water volumes. R. Akkurt, H. J. Vinegar, P. N. Tutunjian, and A. J. Guillory, "NMR logging of natural gas reservoirs," Paper N, Transactions of the Society of Professional Well Log Analysts 36th Annual Logging Symposium (1995).
In the same paper, Akkurt et al. introduced a detailed method for identifying and typing hydrocarbons. That method is called the Differential Spectrum Method (hereinafter, "DSM"). Later, an improvement to the DSM method, known as Time Domain Analysis (hereinafter, "TDA"), was developed by M. G. Prammer, E. D. Drack, J. C. Bouton, J. S. Gardner, G. R. Coates, R. N. Chandler, and M. N. Miller, "Measurements of clay-bound water and total porosity by magnetic resonance logging," SPE Paper 35622, presented at the Society of Petroleum Engineers Annual Technical Conference and Exhibition (1996).
The DSM and TDA methods were both developed for use with tools having a fixed magnetic field gradient (such as the tool available under the trademark MRIL.RTM., by Numar Corporation, of Malvern, Pa.). More recently, another NMR-only method of detecting gas, known as the Echo Ratio Method (hereinafter, "ERM"), was developed by Flaum et al. C. Flaum, R. L. Kleinberg, M. D. Hurlimann, "Identification of gas with the Combinable Magnetic Resonance tool (CMR*)," Paper L, Transactions of the Society of Professional Well Log Analysts 37th Annual Logging Symposium (1996). ERM uses a CMR tool which has a saddle point distribution of magnetic field gradients. ERM identifies gas using apparent diffusion constants computed from the ratios of two T.sub.2 -decay curves acquired with different echo spacings.
These NMR-only methods for calculating porosity and other parameters have various disadvantages. First, these methods work best with a tool that has a fixed or saddle point distribution of magnetic field gradients. Thus, these methods are limited by the type of NMR tool used to acquire data. Second, the NMR-only methods (e.g., ERM) may require data from two NMR measurements having different CPMG sequences. Third, the NMR-only methods require that the gas be appreciably polarized, which means long wait times and slow logging speeds. And fourth, total porosity derivations from NMR-only techniques tend to be computationally complex.
The presence of gas also adversely effects the calculation of density-derived total porosity .phi..sub.density. Unlike NMR-derived total porosity .phi..sub.nmr, which underestimates true total porosity, density-derived total porosity overestimates true total porosity when gas is present in the formation. Thus, in a gas bearing zone, .phi..sub.nmr will be less than .phi..sub.density and the difference between the two porosity logs will be proportional to the gas saturation in the zones. The difference effect is analogous to the "neutron-density" crossover effect in gas zones. The same effect can occur when there is gas condensate or light oil in the formation. However, the magnitude of the effect is reduced. The use of neutron-density logs for gas detection is not reliable because the effects of shale and thermal neutron absorbers on the neutron-density log response can totally suppress the crossover effect. Also, neutron-density-derived total porosities can be inaccurate because of mineralogy effects on the neutron tool response.
Furthermore, conventional calculation of water saturation in shaly formations require knowledge of the formation factor F and cation exchange capacity per unit volume Q.sub.v. Obtaining this knowledge requires core sample measurements. Such core sample measurements, however, are inconvenient, time-consuming, and costly because they require that core samples be brought to the surface and analyzed, usually at an off-site laboratory. And, the cost generally scales with the number of core samples analyzed, which at times can be very large. Therefore, immediate on-site valuation of Q.sub.v and F are precluded using conventional evaluation techniques.
In view of the foregoing, it is an object of this invention to provide methods for accurately determining gas-corrected flushed zone and virgin zone parameters that characterize zones in a formation, even a shaly or gas bearing formation.
It is also an object of this invention to provide methods that allow immediate on-site valuation of formations, without performing uphole core sample analysis.
It is also an object of this invention to provide methods that accurately determine such parameters using nearly any conventional NMR tool, including fixed gradient tools and saddle point tools that have a distribution of magnetic field gradients.
It is yet another object of this invention to provide methods for determining gas-corrected total porosity and flushed zone gas saturation by combining NMR and density log measurements.
It is yet a further object of this invention to combine NMR measurements with other open hole logs to determine critical petrophysical parameters, such as virgin formation hydrocarbon saturation and permeability, needed in the estimation of hydrocarbon reserves and producibility.
It is yet an additional object of this invention to estimate the uncertainty of the magnitudes of the petrophysical parameters determined in accordance with this invention.